A system having air fuel ratio sensors located at upstream and downstream sides of the catalyst located in an exhaust gas passage of the internal combustion engine, for example, is disclosed in Japanese Patent Laid-Open No. 2-190756 published on Jul. 26, 1990 and entitled "Method and Apparatus for detecting a state of a catalyst". The prior art discloses that the degradation of the catalyst is discriminated by a phase difference, between two O.sub.2 sensors located at upstream and downstream sides of the catalyst used for an exhaust gas purification of an internal combustion engine and judged in such a manner that the catalyst is degraded when the phase difference reaches less than a predetermined value.
The prior art has a following drawback:
The sensor located at the downstream side of the catalyst is affected by electrical noises, for example, ignition noise, so that this sensor can not give accurate information of exhaust gases flowing through the sensor. Accordingly, the degradation of the catalyst can not be detected accurately only by means of the phase difference mentioned above.